 | Philosophical Society of Washington (Washington, D.C.) - Science - 1881 - 902 pages
...as the volume of the latter is to the volume of Hie former. But these volumes or solid contents vary as the cubes of their radii, or as the cubes of their distances from the vertex. Therefore the force of gravity varies inversely as the cubes of the distances.... | |
 | Joseph Anthony Gillet - Astronomy - 1882 - 496 pages
...surfaces of two spheres are to each other as the squares of their radii or diameters ; and the volumes of two spheres are to each other as the cubes of their radii or diameters. Distances on the surface of a sphere are usually denoted in degrees. A degree is ¥£D of... | |
 | George Albert Wentworth - 1884 - 372 pages
...circles, the first having a radius of 18 feet, and the other a radius of 24 feet. 13. The volumes of two spheres are to each other as the cubes of their radii. In what ratio are the volumes of two spheres having radii of 8 feet and 12 feet ? 14. Of two moving... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...equal to JD, and R3 equal to ^D3, and consequently, V = ^D3; hence, the volumes of spheres are in esieh other as the cubes of their radii, or as the cubes of their ditim,etert1. Scholium. If the figure EBDF, formed by drawing lines from the extremities of the arc... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...D' the diameters of two spheres. Then by § 738, V V 4frR'3~ ''R's' and D'3 That is, the volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 740. COROLLARY V. Let P and K denote the volume and area of the base of a spherical pyramid, and V... | |
 | George Albert Wentworth, George Anthony Hill - Arithmetic - 1887 - 448 pages
...the dome, at 60 cents per foot. Two cubes are to each other (in volume) as the cubes of their edges. Two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. The surfaces of two spheres are as the squares of their radii, or as the squares of their diameters.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...42. COROLLARY 1. The result of this proposition may be formulated, 43. COROLLARY II. The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. PROPOSITION XII.—THEOREM. 44. The volume of a spherical sector is equal to the area of the zone which... | |
 | William Chauvenet - Geometry - 1887 - 342 pages
...proposition may be formulated, v = $K£S. Corollary II. The volumes of two spheres are to each other aa the cubes of their radii, or as the cubes of their diameters. PROPOSITION XII. The volume of a spherical sector is equal to the area of the zone which forms its... | |
 | George Albert Wentworth - Algebra - 1888 - 238 pages
...circles, the first having a radius of 18 feet, and the other a radius of 24 feet・ 13 The volumes of two spheres are to each other as the cubes of their radii・ In what ratio are the volumes of two spheres having radii of 8 feet and 12 feet ? 14 Of two moving... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...47rR', (790) .-.V=f7rR'; (796) or, if D denotes the diameter, V = 17TD'. 799. COR. 3. The volumes of two spheres are to each other as the cubes of their radii. 800. COR. 4. Tiie volume of a spherical sector is equal to the area of the zone which forms its base... | |
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The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 
